Python 代码

a, b, c, d, k = map(int, input().split())

N = 2010
res = 0
mod = 100003
fact = [0] * N
infact = [0] * N

def qmi(a, b, p):
    res = 1
    while b:
        if b & 1: 
            res = res * a % p
        a = a * a % p
        b >>= 1
    return res

fact[0] = 1
infact[0] = 1

for i in range(1, N):
    fact[i] = fact[i-1] * i % mod
    infact[i] = infact[i-1] * qmi(i, mod-2, mod) % mod

def C(a, b):
    global mod
    return fact[a] * (infact[b] * infact[a-b] % mod) % mod

def A(a, b):
    global mod
    return fact[a] * infact[a-b] % mod

for i in range(k+1):
    if i > min(a, b): break
    if k - i > min(a+c-i, d): continue
    res = (res + (C(a, i) * A(b, i) % mod) * (C(a+c-i, k-i) * A(d, k-i) % mod)) % mod
print(res)